Boundary behavior of the Bergman curvature in strictly pseudoconvex polyhedral domains

Kang-Tae Kim and Jiye Yu

Vol. 176 (1996), No. 1, 141–163

DOI: 10.2140/pjm.1996.176.141

Abstract

In this article, we present an explicit description of the boundary behavior of the holomorphic curvature of the Bergman metric of bounded strictly pseudoconvex polyhedral domains with piecewise C² smooth boundaries. Such domains arise as an intersection of domains with strongly pseudoconvex domains with C² smooth boundaries, creating normal singularities in the boundary. Our results in particular yield an optimal generalization of the well-known theorem of Klembeck, in terms of the boundary regularity. As an application, we demonstrate generalization of several theorems which were previously known only for the cases of eveywhere C^∞ (essentially) smooth boundaries.

Mathematical Subject Classification

Primary: 32H10

Secondary: 32F15

Milestones

Received: 15 March 1994

Revised: 7 February 1995

Published: 1 November 1996